I would buy a $25 volt/ohm meter, most sensors can be tested with this meter.
90% of sensors replaced by DIYers were not bad, but don't feel too bad since 50% of sensors replaced by professional mechanics were not bad either, although I think the later were to PAD THE BILL, lol.
Compression test, dry, and then wet(oil added) can tell you if rings or valve are questionable.
Compression gauge(screw on type) runs about $25 as well
Only get screw on type, they screw into spark plug hole.
You can also rent them.
A vacuum gauge is also not expensive, $15, and can tell you alot about an engine.
Good read here: Technical Articles: Engine testing with a Vacuum Gauge - at Greg's Engine & Machine
The 3 above tools are generic, can be used on old and new engines from any manufacturer.
MAF sensor test and clean here: Ford Ranger Mass Air Flow Cleaning, Removal and Installation
O2 sensor generates its own voltage, .1 to .9 volts after engine is warmed up, O2 sensor can't work until it is above 600degF.
IAC valve can be removed and cleaned, while it is removed connect it to its wiring then turn on the key, it should open all the way then close slightly.
Turn off key and it should close all the way.
TPS is the same as a light dimmer or volume control, a variable resistor, it has 3 wires, upper wire has 5 volts from computer, center wire is the control voltage back to computer.
When throttle is closed center wire should have .6 to .9volts
As you slowly open throttle, center wire voltage should go up, no jumping around or drop outs, when you get to WOT(wide open throttle) voltage on center wire should be above 4.5volts.
Operate throttle open and closed a few times, you are looking for dead spots, or jumps in voltage.
You test wires while they are in place, use sewing pins to pierce wires to read voltage, pins make small holes that won't cause problems, if testing 2 wires next to each other make sure pins can't short together.
EGR valve is easily tested with a vacuum hose, start engine, unplug vacuum hose on EGR valve, there should be NO vacuum in that hose, if there is then the EGR modulator is bad.
Now add your own vacuum hose to EGR valve, suck on that hose, engine should start to stumble as EGR valve opens, release vacuum on hose, engine should start idling normal again, repeat a few times, if idle stumbles and recovers then EGR valve is fine.
But they always need to be cleaned, and with your rich running I would say it would be worthwhile.
$9 fuel filter is always a good investment after getting a used vehicle.
Volt meters are set for DC volts for vehicles, 20vDC if that is a setting on the meter.
OHMs are resistance, if you set meter to 1,000ohms(1k ohms) and touch the 2 probes together you will see 0 ohms, a dead short, no resistance.
If you put one probe on one end of a wire and the other probe on the other end of the same wire you should see 0 ohms as well, meaning wire is OK not broken, if it shows high ohms it could have a corrode connection somewhere.
Alligator clips are handy to have as well, these hold meter probes to wires or pins as needed